Electric polarization in a Chern insulator

TL;DR

This paper generalizes the concept of electric polarization to Chern insulators, addressing challenges due to edge states and providing both theoretical and numerical insights into bulk-edge relationships.

Contribution

It introduces a method to define polarization in Chern insulators, accounting for edge state occupation discontinuities, and supports it with numerical calculations.

Findings

Bulk current relates to bulk polarization differences.

Surface charge depends on edge state occupancy.

Numerical models support the theoretical framework.

Abstract

We extend the Berry-phase concept of polarization to insulators having a non-zero value of the Chern invariant. The generalization to such Chern insulators requires special care because of the partial occupation of chiral edge states. We show how the integrated bulk current arising from an adiabatic evolution can be related to a difference of bulk polarizations. We also show how the surface charge can be related to the bulk polarization, but only with a knowledge of the wavevector at which the occupancy of the edge state is discontinuous. Furthermore we present numerical calculations on a model Hamiltonian to provide additional support for our analytic arguments.